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Question 462106: Using the graph, which of these ordered pairs is the best estimate of the solution of the system y = 3x + 2 and y = -1/4 x + 1?
Answer by math-vortex(648)   (Show Source):
You can put this solution on YOUR website! Using the graph, which of these ordered pairs is the best estimate of the solution of the system y = 3x + 2 and y = -1/4 x + 1?=================================
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You haven't given us any ordered pairs to choose from, but I will show you how to solve this system and you can choose from your list.
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These are two linear equations. Their graphs are straight lines. Their solution will be an ordered pair (x,y) for the point at which the two lines intersect.
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Substitution is a good technique for solving this system because both equations are written as "y = ..."
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Since we are looking for a specific point of intersection, we want an x-value and a y-value that makes both equations true. Since y is equivalent to (3x + 2) AND (-1/4 x + 1), we can say that these expressions are equal to each other. Algebraically, we say
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3x + 2 = -1/4 x + 1
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Now we solve this new equation for x. Add 1/4 x to both sides.
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3x + 2 + 1/4 X = 1
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Subtract 2 from both sides.
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13/4 x = 1 - 2
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13/4 x = -1
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Multiply both sides by 4/13 (the reciprocal of 13/4).
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x = - 4/13
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We now know that the lines intersect when x = - 4/13. We can find the y-value of the intersection point by substituting -4/13 for x in one of our original equations.
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y = -1/4 x + 1
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y = (-1/4)(-4/13) + 1
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y = 1/13 + 1
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y = 14/13
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The solution to your system of equations is (-4/13, 14/13).
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Hope this helps!
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Ms.Figgy
math.in.the.vortex
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